Details

sample106.0ms

Algorithm

intervals

Results

44.0ms	259×	body	10240	exit
31.0ms	107×	body	1280	valid
14.0ms	80×	body	640	valid
4.0ms	35×	body	320	valid
1.0ms	21×	body	160	valid
0.0ms	13×	body	80	valid

simplify47.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 7 (45.0ms)

Iter	Nodes	Cost
0	15	9
1	24	9
2	32	9
3	44	9
4	63	9
5	179	9
6	1184	9
7	5001	7

prune6.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 0.8b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma 1 1 (exp (+ x x)))
0.7b	(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
4×	`add-exp-log` `add-cbrt-cube`
3×	`associate-/r` `associate-/l`
2×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `fma-udef` `div-inv` `expm1-udef`

Counts

2 → 40

Calls

2 calls:

1.0ms	(fma 1 1 (exp (+ x x)))
3.0ms	(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

series91.0ms

Counts

2 → 6

Calls

2 calls:

21.0ms	(fma 1 1 (exp (+ x x)))
70.0ms	(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

simplify75.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (70.0ms)

Iter	Nodes	Cost
0	150	395
1	512	351
2	2464	344
3	5002	343

prune123.0ms

Filtered

46 candidates to 39 candidates (84.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	44	2	46
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	44	3	47

Merged error: 0.7b

Counts

47 → 3

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
0.0b	(- x (* 1/3 (pow x 3)))
0.1b	(* 1/3 (pow x 3))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

88×	`add-sqr-sqrt`
72×	`prod-diff`
52×	`*-un-lft-identity`
49×	`associate-r`
47×	`add-cube-cbrt`
20×	`unswap-sqr`
17×	`unpow-prod-down` `cube-prod`
13×	`associate-l`
9×	`sqr-pow`
8×	`add-exp-log`
5×	`pow1` `unpow3` `add-cbrt-cube` `add-log-exp` `difference-of-squares`
4×	`cube-mult` `*-commutative`
3×	`expm1-log1p-u` `fma-neg` `prod-exp` `log1p-expm1-u`
2×	`distribute-lft-out--`
1×	`pow-to-exp` `sub-neg` `flip3--` `distribute-rgt-out--` `diff-log` `pow-prod-down` `pow-exp` `flip--` `cbrt-unprod` `fma-udef`

Counts

3 → 141

Calls

3 calls:

1.0ms	(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
13.0ms	(- x (* 1/3 (pow x 3)))
8.0ms	(* 1/3 (pow x 3))

series173.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
80.0ms	(- x (* 1/3 (pow x 3)))
40.0ms	(* 1/3 (pow x 3))

simplify93.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	532	1676
1	1991	877
2	5002	877

prune186.0ms

Filtered

150 candidates to 54 candidates (36.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	148	2	150
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	149	4	153

Merged error: 0.7b

Counts

153 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(- x (* 1/3 (pow x 3)))
0.0b	(+ (* (pow x 5) 2/15) (- x (* 1/3 (pow x 3))))
0.1b	(* (pow x 5) 2/15)
0.1b	(* 1/3 (pow x 3))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

166×	`add-sqr-sqrt`
144×	`prod-diff`
115×	`*-un-lft-identity`
94×	`add-cube-cbrt`
91×	`associate-r`
74×	`associate-+r+`
41×	`associate-l`
38×	`unswap-sqr`
37×	`unpow-prod-down`
29×	`cube-prod`
19×	`sqr-pow`
18×	`fma-def`
14×	`add-exp-log`
11×	`add-log-exp`
9×	`*-commutative`
8×	`pow1` `unpow3` `add-cbrt-cube`
7×	`cube-mult`
6×	`prod-exp` `distribute-lft-out` `distribute-lft-out--`
5×	`difference-of-squares`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-neg`
2×	`pow-to-exp` `sub-neg` `diff-log` `pow-prod-down` `pow-exp` `sum-log` `cbrt-unprod`
1×	`+-commutative` `associate-+r-` `flip3--` `distribute-rgt-out--` `flip3-+` `flip--` `flip-+`

Counts

4 → 272

Calls

4 calls:

13.0ms	(- x (* 1/3 (pow x 3)))
38.0ms	(+ (* (pow x 5) 2/15) (- x (* 1/3 (pow x 3))))
6.0ms	(* (pow x 5) 2/15)
8.0ms	(* 1/3 (pow x 3))

series230.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(- x (* 1/3 (pow x 3)))
59.0ms	(+ (* (pow x 5) 2/15) (- x (* 1/3 (pow x 3))))
47.0ms	(* (pow x 5) 2/15)
42.0ms	(* 1/3 (pow x 3))

simplify119.0ms

Algorithm

egg-herbie

Counts

284 → 284

Iterations

Useful iterations: 2 (95.0ms)

Iter	Nodes	Cost
0	843	2589
1	2962	1447
2	5002	1443

prune405.0ms

Filtered

284 candidates to 116 candidates (40.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	282	2	284
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	284	4	288

Merged error: 0.7b

Counts

288 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(log1p (+ (* (pow x 5) 2/15) (- x (* 1/3 (pow x 3)))))
0.1b	(* (pow x 5) 2/15)
0.1b	(expm1 (log1p (+ (* (pow x 5) 2/15) (- x (* 1/3 (pow x 3))))))
0.1b	(* 1/3 (pow x 3))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
15×	`associate-r`
14×	`add-exp-log`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`associate-l`
8×	`pow1` `unpow-prod-down` `add-cbrt-cube`
7×	`unswap-sqr`
6×	`prod-exp`
5×	`expm1-log1p-u` `log1p-expm1-u`
4×	`cube-prod` `add-log-exp` `sqr-pow`
2×	`pow-to-exp` `expm1-log1p` `pow-prod-down` `pow-exp` `*-commutative` `cbrt-unprod`
1×	`cube-mult` `log1p-udef` `unpow3` `log1p-expm1` `expm1-udef`

Counts

4 → 85

Calls

4 calls:

1.0ms	(log1p (+ (* (pow x 5) 2/15) (- x (* 1/3 (pow x 3)))))
6.0ms	(* (pow x 5) 2/15)
1.0ms	(expm1 (log1p (+ (* (pow x 5) 2/15) (- x (* 1/3 (pow x 3))))))
8.0ms	(* 1/3 (pow x 3))

series351.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(log1p (+ (* (pow x 5) 2/15) (- x (* 1/3 (pow x 3)))))
54.0ms	(* (pow x 5) 2/15)
159.0ms	(expm1 (log1p (+ (* (pow x 5) 2/15) (- x (* 1/3 (pow x 3))))))
36.0ms	(* 1/3 (pow x 3))

simplify52.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	381	522
1	1552	466
2	5002	446

prune259.0ms

Filtered

97 candidates to 69 candidates (71.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	95	2	97
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	96	5	101

Merged error: 0.7b

Counts

101 → 5

regimes23.0ms

Accuracy

0% (0.1b remaining)

Error of 0.6b against oracle of 0.5b and baseline of 0.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	6
1	13	6
2	13	6

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.3s	7308×	body	10240	exit
998.0ms	3351×	body	1280	valid
423.0ms	2365×	body	640	valid
132.0ms	1199×	body	320	valid
47.0ms	677×	body	160	valid
15.0ms	408×	body	80	valid